Now to compute the conservative binding potential of the two-body system, we ignore the radiation modes and decompose the potential modes in the Kaluza-Klein (KK) parameterization [1]}, [2]}. In this, the different components of metric \(g_{\mu \nu }\)  (\(=\eta _{\mu \nu }+H_{\mu \nu }\) ) are encoded in three fields, a scalar \(\mathbf {\phi }\) , a 3-dimensional vector \(\mathbf {A}_i\)  and a 3-dimensional symmetric rank two tensor \(\mathbf {\sigma }_{ij}\) . The decomposition is given by,
\(g_{\mu \nu } =\begin{pmatrix}e^{2\mathbf {\phi }/c^2} \,\,\, & -e^{2\mathbf {\phi }/c^2} \frac{\mathbf {A}_j}{c^2}\\-e^{2\mathbf {\phi }/c^2} \frac{\mathbf {A}_i}{c^2} \,\,\,\,\,\, & -e^{-2\mathbf {\phi }/c^2}\mathbf {\gamma }_{ij}+e^{2\mathbf {\phi }/c^2} \frac{\mathbf {A}_i}{c^2}\frac{\mathbf {A}_j}{c^2}\end{pmatrix}\, ,\) 
